LCM for 6, 8 and 36

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What's the Least Common Multiple (LCM) of 6, 8 and 36?

Answer

LCM of 6, 8 and 36 is
72

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 6 = 12, 72 ÷ 8 = 9, 72 ÷ 36 = 2 — and 12, 9 and 2 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/6 by 12 and of y/8 by 9 and of z/36 by 2.

6 = 2 × 3

8 = 23

36 = 22 × 32

Prime6836Highest power
22232223
33—3232

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 23 × 32 = 72

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LCM Table

1st2nd3rdLCM
6821168
6822264
6823552
682424
6825600
6826312
6827216
6828168
6829696
6830120
6831744
683296
6833264
6834408
6835840
683672
6837888
6838456
6839312
6840120
6841984
6842168
68431,032
6844264
6845360
6846552
68471,128
684848
68491,176
6850600

FAQ

What's the Least Common Multiple (LCM) of 6, 8 and 36?

LCM of 6, 8 and 36 is 72

How to find the LCM of 6, 8 and 36 by prime factorization?

Take every prime that appears in 6, 8 and 36 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 6, 8 and 36 two numbers at a time?

Yes. The LCM of 6 and 8 is 24, and the LCM of 24 and 36 is 72 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 72 divisible by 6, 8 and 36?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 6, 72 ÷ 8 and 72 ÷ 36 all come out whole. Any other common multiple of 6, 8 and 36 is a multiple of 72.

See Also